Converting between Fractions and Decimals Worksheets - Free Printable

Explanation:
Let’s solve each part step by step.

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Part A: Convert decimals to fractions

1) 7.43
This is 7 and 43 hundredths → $7 \frac{43}{100} = \frac{743}{100}$
(7 × 100 = 700; 700 + 43 = 743)

2) 0.09
9 hundredths → $\frac{9}{100}$

3) 6.9
6 and 9 tenths → $6 \frac{9}{10} = \frac{69}{10}$
(6 × 10 = 60; 60 + 9 = 69)

4) 3.2
3 and 2 tenths → $3 \frac{2}{10} = \frac{32}{10} = \frac{16}{5}$ (simplified), but unless simplification is required, we can leave as $\frac{32}{10}$. However, standard practice is to simplify if possible. Let’s keep simplified: $\frac{16}{5}$

But wait — the worksheet likely expects *exact* decimal-to-fraction conversion without necessarily simplifying (since in part B they show unsimplified forms like 521/100). So for consistency, we’ll write as improper fraction over power of 10 first, then simplify only if obvious.

Let’s check pattern in part B:
- 5.21 ↔ 521/100 → not simplified
- 9.35 ↔ 521/100? No — wait, matching shows 9.35 ↔ 935/100 (but they wrote 521/100 next to 5.21). So yes, they use numerator = decimal × 100 (for two decimals), etc.

So best to write as improper fraction with denominator 10, 100, or 1000 depending on decimal places.

Let’s do that:

1) 7.43 → 2 decimal places → $\frac{743}{100}$
2) 0.09 → 2 decimal places → $\frac{9}{100}$
3) 6.9 → 1 decimal place → $\frac{69}{10}$
4) 3.2 → 1 decimal place → $\frac{32}{10}$
5) 1.41 → 2 decimals → $\frac{141}{100}$
6) 8.07 → 2 decimals → $\frac{807}{100}$
7) 2.25 → 2 decimals → $\frac{225}{100} = \frac{9}{4}$, but again, likely expect $\frac{225}{100}$ (since part B uses unsimplified). We'll use $\frac{225}{100}$ for now.
8) 0.3 → 1 decimal → $\frac{3}{10}$

But let’s hold — maybe they want simplified? Check part C: options include simplified fractions like 211/25, 18/5, etc. So simplification is expected in final answers.

Let’s simplify where possible:

1) 7.43 = 743/100 → 743 and 100 share no common factor (743 is prime? 743 ÷ 7 = 106.14, ÷13=57.15, ÷17=43.7, ÷19=39.1 — actually 743 is prime), so leave as 743/100

2) 0.09 = 9/100 — already simplified

3) 6.9 = 69/10 — 69 and 10 share no factor (69 = 3×23), so 69/10

4) 3.2 = 32/10 = 16/5 → simplify → 16/5

5) 1.41 = 141/100 — 141 = 3×47, 100 = 2²×5² → no common factor → 141/100

6) 8.07 = 807/100 — 807 ÷ 3 = 269, so 807 = 3×269; 100 not divisible by 3 → 807/100

7) 2.25 = 225/100 = divide numerator & denominator by 25 → 9/4 → 9/4

8) 0.3 = 3/10 — simplified → 3/10

We’ll record these.

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Part B: Match each decimal with its equivalent fraction

Given:
i) 5.21
ii) 9.35
iii) 0.8

Options:
• 4/5
• 521/100
• 187/20

Let’s convert each decimal:

i) 5.21 = 521/100 → matches second option ✔
ii) 9.35 = 935/100 = simplify: divide numerator & denominator by 5 → 187/20 → matches third option ✔
iii) 0.8 = 8/10 = 4/5 → matches first option ✔

So:
i ↔ 521/100
ii ↔ 187/20
iii ↔ 4/5

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Part C: Which fraction equals 4.22?

4.22 = 422/100 = simplify.

Divide numerator and denominator by 2:
422 ÷ 2 = 211
100 ÷ 2 = 50
→ 211/50

Check options:

a) 211/25 = 8.44 ✘
b) 18/5 = 3.6 ✘
c) 211/50 = 4.22 ✔
d) 1/5 = 0.2 ✘

So answer is c) 211/50

Now compile all answers clearly.

Final Answer:
A)
1) 743/100
2) 9/100
3) 69/10
4) 16/5
5) 141/100
6) 807/100
7) 9/4
8) 3/10

B)
i) 5.21 ↔ 521/100
ii) 9.35 ↔ 187/20
iii) 0.8 ↔ 4/5

C) c) 211/50